Are the Contained-Event and Through-Going Muon Spectra Consistent? A Two-Fit Comparison

Two IceCube event selections measuring the same diffuse neutrino sky return different power-law descriptions: contained starting events favour a soft spectrum, through-going muon tracks a harder one. This paper quantifies the disagreement with elementary statistics. The spectral indices differ by 0.59, with a combined uncertainty of 0.215, a tension of 2.74 standard deviations. The two central power laws cross at 473 TeV: below it the soft fit predicts more flux, by a factor 9.73 at 10 TeV; above it the hard fit takes over, with the flux ratio falling to 0.643 at 1 PeV. A tension at the level of 2.7 standard deviations, between selections with different systematics, energy ranges and flavour mixtures, is evidence for spectral structure or for an unmodelled systematic — it is not yet evidence that either measurement is wrong. The study is computed from stated assumptions, not measured.